Hey! How are you? My name is Maria, 19 years old. Yesterday broke up with a guy, looking for casual sex.
Write me here and I will give you my phone number - *pofsex.com*
My nickname - Lovely

The given angles 3 and 4 shares a common arm, therefore the angles are known as Adjacant Angles
(4/5)/(2/3)=4/5*3/2=12/10=1 1/5
two fractions dividing is the same as two fractions multiplying with the second fraction flipped around
1 1/5 yards per second
Answer:x=-8
Step-by-step explanation:
12(x/4+2/3)=12(x/6)
3x+8=2x
3x-2x=-8
x=-8
Answer:

Given expression is
![\rm :\longmapsto\:\displaystyle\lim_{n \to \infty }\rm \bigg[\dfrac{1}{3} + \dfrac{1}{ {3}^{2} } + \dfrac{1}{ {3}^{3} } + - - + \dfrac{1}{ {3}^{n} } \bigg]](https://tex.z-dn.net/?f=%5Crm%20%3A%5Clongmapsto%5C%3A%5Cdisplaystyle%5Clim_%7Bn%20%5Cto%20%20%5Cinfty%20%7D%5Crm%20%5Cbigg%5B%5Cdfrac%7B1%7D%7B3%7D%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7B2%7D%20%7D%20%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7B3%7D%20%7D%20%20%2B%20%20-%20%20-%20%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7Bn%7D%20%7D%20%20%5Cbigg%5D)
Let we first evaluate

Its a Geometric progression with



So, Sum of n terms of GP series is

![\rm :\longmapsto\:S_n = \dfrac{1}{3} \bigg[\dfrac{1 - {\bigg[\dfrac{1}{3} \bigg]}^{n} }{1 - \dfrac{1}{3} } \bigg]](https://tex.z-dn.net/?f=%5Crm%20%3A%5Clongmapsto%5C%3AS_n%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Cbigg%5B%5Cdfrac%7B1%20-%20%20%7B%5Cbigg%5B%5Cdfrac%7B1%7D%7B3%7D%20%5Cbigg%5D%7D%5E%7Bn%7D%20%7D%7B1%20-%20%5Cdfrac%7B1%7D%7B3%7D%20%7D%20%5Cbigg%5D)
![\rm :\longmapsto\:S_n = \dfrac{1}{3} \bigg[\dfrac{1 - {\bigg[\dfrac{1}{3} \bigg]}^{n} }{\dfrac{3 - 1}{3} } \bigg]](https://tex.z-dn.net/?f=%5Crm%20%3A%5Clongmapsto%5C%3AS_n%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Cbigg%5B%5Cdfrac%7B1%20-%20%20%7B%5Cbigg%5B%5Cdfrac%7B1%7D%7B3%7D%20%5Cbigg%5D%7D%5E%7Bn%7D%20%7D%7B%5Cdfrac%7B3%20-%201%7D%7B3%7D%20%7D%20%5Cbigg%5D)
![\rm :\longmapsto\:S_n = \dfrac{1}{3} \bigg[\dfrac{1 - {\bigg[\dfrac{1}{3} \bigg]}^{n} }{\dfrac{2}{3} } \bigg]](https://tex.z-dn.net/?f=%5Crm%20%3A%5Clongmapsto%5C%3AS_n%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Cbigg%5B%5Cdfrac%7B1%20-%20%20%7B%5Cbigg%5B%5Cdfrac%7B1%7D%7B3%7D%20%5Cbigg%5D%7D%5E%7Bn%7D%20%7D%7B%5Cdfrac%7B2%7D%7B3%7D%20%7D%20%5Cbigg%5D)
![\bf\implies \:S_n = \dfrac{1}{2}\bigg[1 - \dfrac{1}{ {3}^{n} } \bigg]](https://tex.z-dn.net/?f=%5Cbf%5Cimplies%20%5C%3AS_n%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%5B1%20-%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7Bn%7D%20%7D%20%5Cbigg%5D)
<u>Hence, </u>
![\bf :\longmapsto\:\dfrac{1}{3} + \dfrac{1}{ {3}^{2} } + \dfrac{1}{ {3}^{3} } + - - + \dfrac{1}{ {3}^{n} } = \dfrac{1}{2}\bigg[1 - \dfrac{1}{ {3}^{n} } \bigg]](https://tex.z-dn.net/?f=%5Cbf%20%3A%5Clongmapsto%5C%3A%5Cdfrac%7B1%7D%7B3%7D%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7B2%7D%20%7D%20%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7B3%7D%20%7D%20%20%2B%20%20-%20%20-%20%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7Bn%7D%20%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%5B1%20-%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7Bn%7D%20%7D%20%5Cbigg%5D)
<u>Therefore, </u>
![\purple{\rm :\longmapsto\:\displaystyle\lim_{n \to \infty }\rm \bigg[\dfrac{1}{3} + \dfrac{1}{ {3}^{2} } + \dfrac{1}{ {3}^{3} } + - - + \dfrac{1}{ {3}^{n} } \bigg]}](https://tex.z-dn.net/?f=%20%5Cpurple%7B%5Crm%20%3A%5Clongmapsto%5C%3A%5Cdisplaystyle%5Clim_%7Bn%20%5Cto%20%20%5Cinfty%20%7D%5Crm%20%5Cbigg%5B%5Cdfrac%7B1%7D%7B3%7D%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7B2%7D%20%7D%20%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7B3%7D%20%7D%20%20%2B%20%20-%20%20-%20%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7Bn%7D%20%7D%20%20%5Cbigg%5D%7D)
![\rm \: = \: \displaystyle\lim_{n \to \infty }\rm \dfrac{1}{2}\bigg[1 - \dfrac{1}{ {3}^{n} } \bigg]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Cdisplaystyle%5Clim_%7Bn%20%5Cto%20%20%5Cinfty%20%7D%5Crm%20%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%5B1%20-%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7Bn%7D%20%7D%20%5Cbigg%5D)
![\rm \: = \: \rm \dfrac{1}{2}\bigg[1 - 0 \bigg]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Crm%20%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%5B1%20-%200%20%5Cbigg%5D)

<u>Hence, </u>
![\purple{\rm :\longmapsto\:\boxed{\tt{ \displaystyle\lim_{n \to \infty }\rm \bigg[\dfrac{1}{3} + \dfrac{1}{ {3}^{2} } + \dfrac{1}{ {3}^{3} } + - - + \dfrac{1}{ {3}^{n} } \bigg]} = \frac{1}{2}}}](https://tex.z-dn.net/?f=%20%5Cpurple%7B%5Crm%20%3A%5Clongmapsto%5C%3A%5Cboxed%7B%5Ctt%7B%20%5Cdisplaystyle%5Clim_%7Bn%20%5Cto%20%20%5Cinfty%20%7D%5Crm%20%5Cbigg%5B%5Cdfrac%7B1%7D%7B3%7D%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7B2%7D%20%7D%20%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7B3%7D%20%7D%20%20%2B%20%20-%20%20-%20%20%2B%20%5Cdfrac%7B1%7D%7B%20%7B3%7D%5E%7Bn%7D%20%7D%20%20%5Cbigg%5D%7D%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%7D%7D)
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
<h3>
<u>Explore More</u></h3>




